suppose we draw 2500 samples of size 100 from a population and compute a 97% confidence interval for each sample. approximately how many of those intervals will contain the population mean?

The general solution is given by: y = c1cos(5x) + c2sin(5x) + 1/25(- cos(ln(sec5x))) + 5xsin(5x)

The most general solution to the original nonhomogeneous differential equation can be found by adding the homogeneous solution and the particular solution together. That is,

y = y_h + y_p

= c1cos(5x) + c2sin(5x) + 1/25(- cos(ln(sec5x))) + 5xsin(5x)

This is the most general solution to the original nonhomogeneous differential equation. We can use the arbitrary constants c1 and c2 to find specific solutions for different initial conditions. The general solution is given by:

y = c1cos(5x) + c2sin(5x) + 1/25(- cos(ln(sec5x))) + 5xsin(5x)

This is the final answer. Note that we have used the terms "general solution" and "arbitrary constants" in our answer, as instructed.

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Answer:

The answer is 4/17

Step-by-step explanation:

Answer:

Answer  = 21 Sacks

Step-by-step explanation:

First, we need to calculate how much flour the baker will use in 20 days:

Amount of flour used per day for 64 loaves = 64 loaves/day x 400 g/loaf = 25,600 g/day

Amount of flour used in 20 days = 25,600 g/day x 20 days = 512,000 g

Next, we need to convert the amount of flour used into kilograms:

512,000 g ÷ 1000 g/kg = 512 kg

Finally, we need to calculate the minimum number of 25 kg sacks the baker should order:

Number of 25 kg sacks = 512 kg ÷ 25 kg/sack ≈ 20.48

Since the baker cannot order a fraction of a sack, he will need to order at least 21 sacks to last him for 20 days.

The charged battery costs 16 dollars, which is denoted as -16. (negative number). The cost for  the savings for using a battery that can be recharged is +14(positive number).

A battery is an electrical energy storage instrument made up of one or more electrochemical cells connected to the outside world. The cathode and anode of a battery are the positive and negative terminals, respectively, when the battery is supplying electricity.                            The battery costs 16 dollars. You save 14 dollars each time you recharge the battery.  The cost of the rechargeable battery as a negative number is -16.The savings for using a battery that can be recharged is +14

The charged battery costs 16 dollars, which is denoted as -16. (negative number). Each refresh saves 14 dollars, which is symbolised as +14. (positive number). The charged battery costs 16 dollars, which is denoted as -16. (negative number). The cost for  the savings for using a battery that can be recharged is +14(positive number).

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Answer:

I believe it's C.

Step-by-step explanation:

The correct equation of p is C. p(x) = x(x - 3)^2(2x + 7)^2. This is because the given polynomial has a zero of multiplicity 2 at x = 3, a zero of multiplicity 1 at x = 0, and a zero of multiplicity 2 at x = -7/2. Therefore, the equation of the polynomial can be written as p(x) = k(x - 3)^2(x)(2x + 7)^2, where k is some constant. Since the leading coefficient of the polynomial is 1, k = 1. Thus, we get the equation p(x) = x(x - 3)^2(2x + 7)^2.

It is option C and not A, B, or D because:

Option A, p(x)= x(x - 3)(2x + 7)^2, has only one factor of (x - 3), but the given polynomial has a factor of (x - 3) squared.

Option B, p(x) x^2(x - 3)(2x + 7), has an extra factor of x^2 that is not present in the given polynomial.

Option D, p(x)= x(x - 3)^2(2x + 7), is very close to the correct answer, but it is missing the factor of (x) that is present in the given polynomial.

Thus, the correct equation of p is C, p(x) = x(x - 3)^2(2x + 7)^2, which includes all the necessary factors and satisfies the given conditions.

Hope this helps you! I'm sorry if it doesn't. If you need more help, ask me! :]

Answer: 490.87 is the answer, rounded to a whole number is 491.

Step-by-step explanation: A≈490.87m²

Solving for A

A=1

4πd2=1

4·π·252≈490.87385m²

Not sure that's really an explanation but... Hope that makes since :)

Answer:

k=11/3

Step-by-step explanation:

Use distributive property.

3k+4=15

Subtract 4 from both sides.

3k=11

Divide 3 from both sides.

k=11/3

Answer: k=11/3 or 3.66

Step-by-step explanation:

3k+4=15 --Distribute 1/3 to 9k and 12.

3k=11 --Subtract 4 from both sides.

k=11/3 or 3.66

Please give brainliest !!

According the given question the value οf x is (b+1)/(d-a).

Tο simplify simply means tο make anything easier. In mathematics, simplifying an equatiοn, fractiοn, οr prοblem means taking it and making it simpler.

Calculatiοns and prοblem-sοlving techniques simplify the issue. Simplifying shοuld have twο essential characteristics: it shοuld be algοrithmic, and it shοuld result in the same simplified fοrm when twο expressiοns fοr the same thing are simplified. These characteristics οf a simplificatiοn apprοach prοvide an algοrithm fοr determining whether twο expressiοns are equivalent.

Here, we have

Given: ax+b=dx-1,  if a≠d

We have tο find the value οf x.

We apply simplificatiοn here and we get

ax+b = dx-1

b + 1 = dx - ax

b +1 = x(d-a)

x = (b+1)/(d-a)

Hence, the value οf x is (b+1)/(d-a).

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The family needs 15 cubic feet of sand to fill the mold completely.

The volume of the square pyramid sand castle mold can be calculated as V = (1/3) * b² * h, where b is the length of one edge of the square base and h is the height from the base to the apex.

In this case, b = 3 feet and h = 5 feet.

Plugging these values into the formula, we get:

V = (1/3) * 3² * 5

V = 15 cubic feet

Therefore, the family needs 15 cubic feet of sand to fill the mold completely.

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The two sets of data are

Set 1: 5, 6, 7, 8, 9, 10, 20

Set 2: 1, 2, 3, 4, 5, 15, 16

The median is a measure of central tendency in a data set that represents the middle value of the data when arranged in order.

To find the median of a data set, we need to arrange the values in ascending or descending order and then find the middle value.

The IQR (Interquartile Range) is a measure of variability in a data set that represents the difference between the 75th percentile (third quartile) and the 25th percentile (first quartile).

To calculate the IQR of a data set, we need to find the values of the first quartile (Q1), and third quartile (Q3), and then subtract Q1 from Q3.

Here we have

Each data set has 7 values, -

The median of set 1 is greater than the median of set 2, -

The IQRs of the data sets are the same.

To create the sets assume a positive value as the median of the data and make sure that the value is in the middle of the data.

Similarly, take another positive value that is greater than the previous value and make sure that the value is also in the middle.

Now arrange the remaining values such that both sets of data have the same IQRs.  

Here are two sets of data that meet the given characteristics:

Set 1: 5, 6, 7, 8, 9, 10, 20

Median: 8

IQR: 4 (Q3 = 9, Q1 = 5)

Set 2: 1, 2, 3, 4, 5, 15, 16

Median: 4

IQR: 4 (Q3 = 5, Q1 = 1)

Therefore,

The two sets of data are

Set 1: 5, 6, 7, 8, 9, 10, 20

Set 2: 1, 2, 3, 4, 5, 15, 16

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Answer:

C. (6r + 5)

Step-by-step explanation:

You would multiply (3r - 7) with (6r + 5) to get the value.

he volume of the drum can be calculated as follows:

Volume of drum = πr²h

= π(4.2m)²(3.5m)

≈ 246.33 m³

To find out how many full bags of wheat can be emptied into the drum, we need to divide the volume of the drum by the volume of one wheat bag:

Number of full bags of wheat = Volume of drum ÷ Volume of one bag

= 246.33 m³ ÷ 5.39 m³

≈ 45.72

Therefore, the circular drum can hold approximately 45 full bags of wheat.

Answer: 45 Full of bags.

Step-by-step explanation:

The volume of the drum can be calculated using the formula for the volume of a cylinder: V = πr^2h, where r is the radius and h is the height.

V = π(4.2m)^2(3.5m)

V ≈ 246.73 m³

To find out how many bags of wheat can be emptied into the drum, we need to divide the volume of the drum by the space required for one bag:

246.73 m³ ÷ 5.39 m³/bag ≈ 45.81 bags

Since we can't have a fraction of a bag, we need to round down to the nearest whole number:

Number of bags = 45

Therefore, 45 full bags of wheat can be emptied into the drum.

The value of the test statistic is -1.75.

To test the claim that the percentage of uninsured patients is under the expected percentage of 32%, we can use a one-sample z-test. The null hypothesis is that the true percentage of uninsured patients is equal to 32%, while the alternative hypothesis is that the true percentage is less than 32%.

Using the sample data, we can calculate the sample proportion of uninsured patients as 40/160 = 0.25. We can then calculate the standard error of the sample proportion as sqrt[(0.32 x 0.68)/160] = 0.0385.

The test statistic can be calculated as (0.25 - 0.32)/0.0385 = -1.75.

To find the p-value associated with this test statistic, we can use a standard normal distribution table or a calculator to find the probability of a z-score less than -1.75. The p-value is approximately 0.04.

Since the p-value is less than the typical significance level of 0.05, we reject the null hypothesis and conclude that there is evidence to support the claim that the percentage of uninsured patients is under the expected percentage of 32%.

Therefore, the correct answer is -1.75, which is the calculated value of the test statistic.

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We can say that after answering the offered question As a result, the equation for the circle with centre (7, -7) and point (11, -3) i[tex](x - 7)2 + (y + 7)2 = 32.[/tex]

An equation is a mathematical statement that proves the equality of two expressions connected by an equal sign '='. For instance, 2x – 5 = 13. Expressions include 2x-5 and 13. '=' is the character that links the two expressions. A mathematical formula that has two algebraic expressions on either side of an equal sign (=) is known as an equation. It depicts the equivalency relationship between the left and right formulas. L.H.S. = R.H.S. (left side = right side) in any formula.

Determine the radius:

The radius of the circle is the distance between the circle's centre (7, -7) and any point on it (11, -3).

We may calculate the distance using the distance formula:

[tex]r = \sqrt((11 - 7)^2 + (-3 - (-7))\\v^2)\\r = \sqrt(4^2 + 4^2)\\r = \sqrt(32) (32)[/tex]

In the standard form equation of a circle, substitute the centre and radius:

A circle with centre (h, k) and radius r has the following standard form equation:

[tex](x - h)^2 + (y - k)^2 = r^2[/tex]

With h = 7, k = -7, and r = sqrt(32), we get:

[tex](x - 7)^2 + (y + 7)^2 = 32[/tex]

As a result, the equation for the circle with centre (7, -7) and point (11, -3) is[tex](x - 7)2 + (y + 7)2 = 32.[/tex]

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The probability of at most one accident in the next 2 hours is 82.15%.

Let X be the number of car accidents in the next 2 hours, and Y be the number of motorcycle accidents in the next 2 hours. Both X and Y follow Poisson distributions, with rates of λX = 0.12 = 0.2 and λY = 0.052 = 0.1, respectively.

To find the probability that there will be at most one accident (either car or motorcycle) in the next 2 hours, we need to find the probability of the events {X + Y = 0} and {X + Y = 1}:

P(X + Y ≤ 1) = P(X + Y = 0) + P(X + Y = 1)

To find these probabilities, we can use the joint Poisson distribution of X and Y:

P(X = i, Y = j) = e^-(λX+λY) * (λXᵃ /a!) * (λYᵇ / b!)

where a and b are non-negative integers.

For X + Y = 0, we have:

P(X + Y = 0) = P(X = 0, Y = 0) = e⁻⁽⁰ ²⁺⁰ ¹⁾  * (0.2⁰ / 0!) * (0.1⁰ / 0!) = e⁻⁰ ³ ≈ 0.7412

For X + Y = 1, we have:

P(X + Y = 1) = P(X = 0, Y = 1) + P(X = 1, Y = 0) = e⁻⁽⁰ ²⁺⁰ ¹⁾ * (0.2⁰/ 0!) * (0.1¹/ 1!) + e⁻⁽⁰ ²⁺⁰ ¹⁾  * (0.2¹/ 1!) * (0.1⁰ / 0!) = 20.20.1*e⁻ ⁰ ³ ≈ 0.0803

Therefore, the probability of there being at most one accident (either car or motorcycle) in the next 2 hours is:

P(X + Y ≤ 1) ≈ 0.7412 + 0.0803 ≈ 0.8215

So the probability of there being at most one accident in the next 2 hours is about 82.15%.

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0.67032

The given data is that car accidents and motorcycle accidents on a stretch of road occur independently and are described by the Poisson distribution at a rate of 0.1 and 0.05 per hour respectively. It is required to find the probability that there will be at most one accident in the next 2 hours.The number of car accidents along the stretch of the road in the next 2 hours is a Poisson distribution with a mean of 0.1 x 2 = 0.2. Similarly, the number of motorcycle accidents in the next 2 hours is a Poisson distribution with a mean of 0.05 x 2 = 0.1.The probability that there will be at most one accident in the next 2 hours is:P(at most one accident in the next 2 hours)=P(no accident in the next 2 hours)+P(one accident in the next 2 hours)= e^(-0.2) (0.2)^0 / 0! + e^(-0.2) (0.2)^1 / 1! + e^(-0.1) (0.1)^0 / 0! + e^(-0.1) (0.1)^1 / 1!= 0.67032Therefore, the probability that there will be at most one accident in the next 2 hours is 0.67032.

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The shape shοwn is a a parallelοgram as  twο sides are parallel and οppοsite angles are same. Thus, οptiοn D is cοrrect.

A parallelοgram is a quadrilateral in which the οppοsite sides are parallel and equal. Parallelοgrams are classified intο three main types: square, rectangle, and rhοmbus, and each οf them has its οwn unique prοperties.

A parallelοgram is a special kind οf quadrilateral that is fοrmed by parallel lines. The angle between the adjacent sides οf a parallelοgram may vary but the οppοsite sides need tο be parallel fοr it tο be a parallelοgram. A quadrilateral will be a parallelοgram if its οppοsite sides are parallel and cοngruent. Hence, a parallelοgram is defined as a quadrilateral in which bοth pairs οf οppοsite sides are parallel and equal.

Given that:

One οf the twο οppοsite sides are equal

The οther twο sides are parallel

These are the traits οf a parallelοgram.

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Complete question:

What type of shape is show below:

Answer: ty

Step-by-step explanation:

Brainliest pls:)

Answer:

a)

=2×5+2×6

=10+12

=22

Ans. GCF (10, 12) = 2

Answer:

Step-by-step explanation:

D.The value of B is equal to -1

The Sun is approximately 9.2661 x 10^7 miles farther than the Moon from Earth.

The distance between the Sun and the Earth is approximately 9.29 x 10^7 miles, and the distance between the Moon and the Earth is approximately 2.389 x 10^5 miles.

To find how much farther the Sun is from the Earth than the Moon, we can subtract the distance between the Moon and the Earth from the distance between the Sun and the Earth:

9.29 x 10^7 miles - 2.389 x 10^5 miles = 9.2661 x 10^7 miles

Therefore, the Sun is approximately 9.2661 x 10^7 miles farther than the Moon from Earth.

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The probability of occurring not more than two flood events in a particular year at that location is approximately 0.546.

The given distribution is λxe-λx! where λ is the expected number of flood events in a year. In order to calculate the probability of not more than two flood events in a particular year at that location.

The expected number of flood events in a year is given by: λ = (5 flood events) / (2 years) = 2.5 flood events per year

The given distribution is:λxe-λx! = 2.5xe-2.5x!

We need to find the probability of occurring not more than two flood events in a particular year at that location.

Therefore, the required probability is:P(x ≤ 2) = P(x = 0) + P(x = 1) + P(x = 2)Here, P(x) represents the probability of x flood events.

The probability of x flood events can be calculated using the Poisson distribution formula:

P(x) = λxe-λx!Substitute λ = 2.5 and x = 0 in the above formula to get:P(0) = (2.5)0e-2.5 / 0! = e-2.5 ≈ 0.082Substitute λ = 2.5 and x = 1 in the above formula to get:P(1) = (2.5)1e-2.5 / 1! = 2.5e-2.5 ≈ 0.206Substitute λ = 2.5 and x = 2 in the above formula to get:P(2) = (2.5)2e-2.5 / 2! = 3.125e-2.5 ≈ 0.258Step 5

Now, add the above probabilities to find the required probability:P(x ≤ 2) = P(0) + P(1) + P(2)≈ 0.082 + 0.206 + 0.258 = 0.546Therefore, the probability of occurring not more than two flood events in a particular year at that location is approximately 0.546.

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The sοlutiοn(s) οn the graph are x = -4, 2.

In mathematics, a graph is a diagram οr visual representatiοn οf facts οr values that is οrdered. The pοints οn a graph are typically used tο depict the relatiοnships between twο οr mοre things. Graph theοry is the study οf graphs, which are mathematical structures that are used tο depict pairwise interactiοns between οbjects. A graph in this sense is made up οf vertices and edges.

A graph is an οrdered graphic οr visual representatiοn οf facts οr values in mathematics. The relatiοnships between twο οr mοre οbjects are οften shοwn by the pοints οn a graph.

The study οf graphs, which are mathematical representatiοns οf pairwise interactiοns between things, is knοwn as graph theοry. Vertices and edges make up a graph in this cοntext.

From the given graph we conclude following -

[tex]\frac{1}{4}x^2 = -\frac{1}{2}x + 2\\x^2 + 2x - 8 = 0\\x^2 + 4x - 2x - 8 = 0\\x(x + 4) - 2(x + 4) = 0\\(x + 4)(x - 2) = 0\\x = 2, -4[/tex]

On the graph, the solutiοns are the x-coοrdinates of the points of intersection

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The circular pan with a 16 inch diameter is 55.94 square inches (256-201.06) larger than the square pan with sides measuring 16 inches.

The area of a circle is given by the formula A=πr2, where r is the radius of the circle. The radius of a circle with a 16 inch diameter is 8 inches. Therefore, the area of this circle is A=π*82=201.06 square inches.

The area of a 16 inch square is given by the formula A=s2, where s is the length of the side of the square. The area of this square is A=162=256 square inches.

Therefore, the circular pan with a 16 inch diameter is 55.94 square inches (256-201.06) larger than the square pan with sides measuring 16 inches.

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Answer:

4.06 cm^2

Step-by-step explanation:

If you draw a line from the top vertex to intersect the base (which is 5.8 cm) at 90 degrees, the line is called the height. You need to calculate the height to determine the area.

So the triangle's height will divide the triangles into 2 smaller right triangles.

For the left right triangle, 2.5 will be hypotenuse

=> 2.5^2 = (height)^2 + (base1)^2

=> (height)^2 = 6.25 - (base1)^2

For the right right triangle, 4 will be hypotenuse

=> 4^2 = (height)^2 + (base2)^2

=> (height)^2 = 16 - (base2)^2

So

6.25 - (base1)^2 = 16 - (base2)^2

We have base1 + base2 = 5.8 => base1 = 5.8 - base2

Substitute

6.25 - (5.8 - base2)^2 = 16 - (base2)^2

6.25 - (33.64 - 11.6base2 + base2^2 = 16 - base2^2

base2^2 - base2^2 + 11.6base2 = 16 + 33.6 - 6.25

11.6base2 = 43.35

base2 = 43.35/11.6 = 3.74

since (height)^2 = 16 - (base2)^2

(height)^2 = 16 - (3.74)^2

height^2 = 2.0124

height = 1.42

so area = 1/2hb = 1/2(1.4)(5.8) = 4.06 cm^2

Answer:

a) The circumference of the cylinder can be found using the formula C = 2πr, where r is the radius of the circular base. Rearranging the formula, we get r = C/2π. To find the circumference, we can use the formula for the curved surface area: A = 2πrh, where h is the height of the cylinder. Substituting the given values, we get:

660 = 2πr(10)

r = 33/π

Now we can find the circumference:

C = 2πr = 2π(33/π) = 66

Therefore, the circumference of the cylinder is 66 cm.

b) The radius of the cylinder is given by r = 33/π, which we already found in part a).

c) The area of one circular base can be found using the formula A = πr^2. Substituting the value of r from part b), we get:

A = π(33/π)^2 = 1089/π

Therefore, the area of one circular base is 1089/π cm^2.

d) The surface area of the cylinder consists of the curved surface area and two circular bases. The area of one circular base was found in part c), so we just need to add the curved surface area to twice the area of one circular base:

Surface area = 2A + 2πrh

Substituting the given values, we get:

Surface area = 2(1089/π) + 2π(33/π)(10) = 2187/π + 660

Therefore, the surface area of the cylinder is 2187/π + 660 cm^2.

Step-by-step explanation:

Answer:

0.85 m

Step-by-step explanation:

Model dimension : Real dimension

3 : 74

x : 21

[tex] \frac{21}{74} = \frac{x}{3} \\ x = 3 \times \frac{21}{74} \\ = \frac{63}{74} \\ = 0.851...[/tex]

Answer:

85.54 cm

Step-by-step explanation:

To find the height of the scale model, we need to use the scale ratio given: 3 : 74. This means that every 3 units on the model represent 74 units on the real building.

First, we need to determine the ratio of the heights. Let x be the height of the scale model. Then:

3 / 74 = x / 21

Solving for x, we get:

x = 21 * 3 / 74

x = 0.8554 m

To convert this to centimeters, we multiply by 100:

x = 85.54 cm

Therefore, the height of the scale model is 85.54 cm to 2 decimal places.

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Answer:

735.1 square meters

Step-by-step explanation:

total surface area (TSA) of a cone can be calculated by using this mathematical expression:

Total surface area (TSA) of a cone = πr(l + r)

Total surface area (TSA) of a cone = πr(l + r)

Total surface area (TSA) of a cone = 3.142 × 6 × (33 + 6)

Total surface area (TSA) of a cone = 3.142 × 6 × (39)

Total surface area (TSA) of a cone = 735.1 square meters.

Answer:

the amount will give 69 percentage of nothing thanks

The amount of fertilizer needed for the garden is 508600 grams.

In the middle of the garden is a pond that is approximately circular with a diameter of 40 m. Therefore, the fertilizer will not be applied in the pond area.

The villagers will only apply the fertilizer in the garden area. The recommended rate of application of the fertiliser is 25 g/m².

Therefore, let's find the fertilizer required for the garden.

area of the garden to be fertilized = area of trapezium - area of a circle

area of the garden to be fertilized = 1 / 2 (a + b)h - πr²

area of the garden to be fertilized = 1 / 2 (124 + 196)135 - 3.14(20)²

area of the garden to be fertilized = 1 / 2 (320)(135) - 1256

area of the garden to be fertilized = 43200 / 2 - 1256

area of the garden to be fertilized = 21600 - 1256

area of the garden to be fertilized = 20344 m²

Therefore,

1 m² = 25 grams

20344 m² = ?

Hence,

amount of fertiliser needed  = 20344 × 25 = 508600 grams

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Answer:

62.85 units

Step-by-step explanation:

s= rΘ

s= 4*5π/3= 20π/3

the perimeter= 20π/3*3

= 20π

= 20*22/7

= 440/7=62.85